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Volevič systems of singular nonlinear partial differential equations. (English) Zbl 0854.35123
The following system of singular nonlinear partial differential equations is studied: $\varphi(t) {\partial u_i\over \partial t}= f_i(t, x, (\mu_0(t) D^k u_j)_{(j, k)\in {\mathfrak N}(i)})+ g_i(t, x),\quad 1\leq i\leq N,$ where $$u= (u_1,\dots, u_N)\in Y^N$$ and $$x\in \Omega$$. Here $$\Omega$$ is an open subset of $$X$$; $$X$$ is a Banach space; moreover, $$D$$ stands for the Fréchet differentiation with respect to $$x$$. The main result of the paper consists in the formulation and proving an existence and uniqueness theorem of the local solution in the ultradifferentiable class. The results obtained are interesting; however, the paper is very technical and includes no application.

##### MSC:
 35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions) 35A10 Cauchy-Kovalevskaya theorems
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##### References:
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